cshell                 package:e1071                 R Documentation

_F_u_z_z_y _C-_S_h_e_l_l _C_l_u_s_t_e_r_i_n_g

_D_e_s_c_r_i_p_t_i_o_n:

     The _c_-shell clustering algorithm, the shell prototype-based
     version (ring prototypes) of the fuzzy _k_means clustering method.

_U_s_a_g_e:

     cshell(x, centers, iter.max=100, verbose=FALSE, dist="euclidean",
            method="cshell", m=2, radius = NULL)

_A_r_g_u_m_e_n_t_s:

       x: The data matrix, were columns correspond to the variables and
          rows to observations.

 centers: Number of clusters or initial values for cluster centers

iter.max: Maximum number of iterations

 verbose: If 'TRUE', make some output during learning

    dist: Must be one of the following: If '"euclidean"', the mean
          square error, if '"manhattan"', the mean absolute error is
          computed. Abbreviations are also accepted.

  method: Currently, only the '"cshell"' method; the c-shell fuzzy
          clustering method

       m: The degree of fuzzification. It is defined for values greater
          than _1_

  radius: The radius of resulting clusters

_D_e_t_a_i_l_s:

     The data given by 'x' is clustered by the fuzzy _c_-shell
     algorithm.

     If 'centers' is a matrix, its rows are taken as the initial
     cluster centers. If 'centers' is an integer, 'centers' rows of 'x'
     are randomly chosen as initial values.

     The algorithm stops when the maximum number of iterations (given
     by 'iter.max') is reached.

     If 'verbose' is 'TRUE', it displays for each iteration the number
     the value of the objective function.

     If 'dist' is '"euclidean"', the distance between the cluster
     center and the data points is the Euclidean distance (ordinary
     kmeans algorithm). If '"manhattan"', the distance between the
     cluster center and the data points is the sum of the absolute
     values of the distances of the coordinates.

     If 'method' is '"cshell"', then we have the _c_-shell fuzzy
     clustering method.

     The parameters 'm' defines the degree of fuzzification. It is
     defined for real values greater than 1 and the bigger it is the
     more fuzzy the membership values of the clustered data points are.

     The parameter 'radius' is by default set to _0.2_ for every
     cluster.

_V_a_l_u_e:

     'cshell' returns an object of class '"cshell"'. 

 centers: The final cluster centers.

    size: The number of data points in each cluster.

 cluster: Vector containing the indices of the clusters where the data
          points are assigned to. The maximum membership value of a
          point is considered for partitioning it to a cluster.

    iter: The number of iterations performed.

membership: a matrix with the membership values of the data points to
          the clusters.

withinerror: Returns the sum of square distances within the clusters.

    call: Returns a call in which all of the arguments are specified by
          their names.

_A_u_t_h_o_r(_s):

     Evgenia Dimitriadou

_R_e_f_e_r_e_n_c_e_s:

     Rajesh N. Dave. _Fuzzy Shell-Clustering and Applications to Circle
     Detection in Digital Images._ Int. J. of General Systems, Vol.
     *16*, pp. 343-355, 1996.

_E_x_a_m_p_l_e_s:

     ## a 2-dimensional example
     x<-rbind(matrix(rnorm(50,sd=0.3),ncol=2),
              matrix(rnorm(50,mean=1,sd=0.3),ncol=2))
     cl<-cshell(x,2,20,verbose=TRUE,method="cshell",m=2)
     print(cl)

     # assign classes to some new data
     y<-rbind(matrix(rnorm(13,sd=0.3),ncol=2),
              matrix(rnorm(13,mean=1,sd=0.3),ncol=2))
     #         ycl<-predict(cl, y, type="both")
             

